Question

Suppose Kaitlin places $6500 in an account that pays 12% interest compounded each year.

Assume that no withdrawals are made from the account.
Follow the instructions below. Do not do any rounding.
(a) Find the amount in the account at the end of 1 year ?
(b) Find the amount in the account at the end of 2 years.?

Answer 1

`\bf ~~~~~~ \textit{Compound Interest Earned Amount \underline{for 1 year}} \\\\ A=P\left(1+(r)/(n)\right)^(nt) \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$6500\\ r=rate\to 12\%\to (12)/(100)\dotfill &0.12\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &1 \end{cases}`

`\bf A=6500\left(1+(0.12)/(1)\right)^(1\cdot 1)\implies A=6500(1.12)\implies A=7280 \\\\[-0.35em] ~\dotfill`

`\bf ~~~~~~ \textit{Compound Interest Earned Amount \underline{for 2 years}} \\\\ A=P\left(1+(r)/(n)\right)^(nt) \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$6500\\ r=rate\to 12\%\to (12)/(100)\dotfill &0.12\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &2 \end{cases}`

`\bf A=6500\left(1+(0.12)/(1)\right)^(1\cdot 2)\implies A=6500(1.12)^2\implies A=8153.6`